### The Algebra of Francesco Ghaligai

The American Mathematical Monthly, Vol. 36, No. 5 (May 1929), 275-278

Summary

In this article Benedict discusses four of the thirteen books that make up the treatise *Summa De Arithmetica* by Francesco Ghaligai, first printed in 1521 and reprinted in 1548 and 1552 (the later with the title *Practica d'Arithmetica*.) The first nine books are arithmetical. The last four are devoted to algebra and give explanations and methods for the extraction of roots and for operations with binomial surds. These are the books on which Benedict concentrates. She claims that Book XIII is "the most interesting in the text. Here we find forty-seven problems not accredited to any other author, though so similar to many in the algebras of the period that we cannot claim originality for Ghaligai." Benedict describes several typical problems and Ghaligai's solutions, but using modern notation and symbols. Here is one example: *Find five numbers in continued proportion such that the sum of the second and fourth shall be* 10, *and the sum of the products of each number by each of the others shall be* 620. As Benedict remarks about this problem and the others, "some of these, without a better symbolism, might puzzle an abler mathematician, and we must admire the ingenuity with which Ghaligai reaches his results."